The US president pulled out of the Quad leaders' meeting - which was due to be held in Sydney next week - to handle negotiations with Congress over the debt ceiling, which needs to be resolved by the end of the month to avoid a catastrophic default.
Prime Minister Anthony Albanese subsequently cancelled the meeting, which also included the Japanese and Indian leaders, on Wednesday after receiving a call from Mr Biden.
Bob Carr said Australians shouldn't believe the Quad "is as significant a forum as some suggest".
"We Australians have been enormously gullible and optimistic about our American partner," the former foreign minister and NSW premier told Sky News.
"We've got to start to factor into our view of the future in this world the prospect that America could be more unpredictable and unreliable.
"The fact the president can cancel the attendance and the meeting can apparently not proceed is a warning about the limits of America's attention span and one that Australia ought to take seriously."
The foreign minister's office said it didn't agree with the comments.
"President Biden is a great friend of Australia. We appreciate that friendship and the role the US plays in the region and in the world," a spokesman for the minister said.
The Indian prime minister will still travel to Australia for a bilateral meeting.
The four leaders are planning to meet on the sidelines of the G7 in Japan this weekend.
Mr Albanese said it was disappointing Mr Biden couldn't visit but he was still invited to in the future.
The president was set to address parliament on Tuesday.
"The Quad is an important body and we want to make sure that it occurs at leadership level and we'll be having that discussion over the weekend," the prime minister said.
Opposition foreign affairs spokesman Simon Birmingham said the shake-up was disappointing but understandable.
"I hope the United States can give real priority to rescheduling that visit and ensuring that that engagement with the Pacific Island leaders happens as soon as possible," he said.
Employment Minister Tony Burke told ABC Radio on Thursday there should not be any concern for Australia's relationship with the US despite the cancelled visit.
"I don't think anyone would question when you've got something like the debt ceiling being negotiated," he said.
"Anyone who knows what negotiations with the debt ceiling are like in the United States understands exactly why President Biden's been in a situation to make him make a decision like this."
Mr Burke said he was hopeful Mr Biden's visit to Australia would be rearranged.
"In terms of the relationship between the countries and the courtesy and the strength of the relationship as allies, that's all there," he said.
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